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"We would like to remind the public that whilst we appreciate the public feeling around this case, it is an offence to breach a court order such as a name suppression, and this includes naming someone who has name suppression on social media."

NewstalkZB's Kate Hawkesby spoke to Justice Minister Andrew Little this morning about the fraught issues of name suppression laws.

"The High Court judge will have to consider what is needed to make sure this chap gets a fair trial.

"We have all just followed the news and then saw the absolute tragedy in the weekend."

It was hard not to feel what the family was going through, he said.

"But really if we want justice to be done we need to leave the police to do their job, continue to gather the evidence, we want the police to present the strongest possible case.

"Part of presenting the strongest possible case is that there is nothing the defence can rely on to upset the trial or allow him to walk away scot free."

For people who were feeling emotional it was important in order for justice to be done for the Millane family that the judicial system be able do its job to "ensure we have the best chance of conviction".

Hawkesby queried what could be done to crack down on suppressed names and details being leaked and published online internationally.

If the police found it was somebody in New Zealand who had disclosed those details that person had committed an offence, Little said.

"It is contempt of court," he said.

"These rules are in place for a reason. It seems a bit odd sometimes."

The accused was entitled to name suppression, he said.

"There is a chance he is not the right person. All this sort of stuff comes into play.

"If we want to do the best for the Millane family and for them to know that New Zealand is a place where justice is done, we've got to follow these rules.

A bill was going through Parliament at the moment which was put together by National MP Chris Finlayson about name suppression

"It kind of tidies up the rules. It doesn't change what they are. But it will certainly make them clear."